13080
domain: N
Properties
Digital Properties
- Digit Count
- 5
- Digit Sum
- 12
- Digital Root
- 3
- Palindromic Number
- no
- Repdigit
- no
- Automorphic
- no
- Kaprekar Number
- no
- Multiplicative Persistence
- 1
Divisibility
- Divisor Count
- 32
- Divisor Sum
- 39600
- Proper Divisor Sum (Aliquot Sum)
- 26520
- Abundant Number
- yes
- Perfect Number
- no
- Deficient Number
- no
- Weird Number
- no
- Untouchable Number
- no
- Primitive Abundant
- no
Derived Values
- Euler's Totient
- 3456
- Möbius Function
- 0
- Radical
- 3270
- Omega Function (Ω)
- 6
- Little Omega Function (ω)
- 4
Special
- Factorial
- no
- Catalan Number
- no
- Bell Number
- no
- Motzkin Number
- no
- Primorial
- no
Figurate Numbers
- Fibonacci Number
- no
- Triangular Number
- no
- Perfect Square
- no
- Perfect Cube
- no
- Pentagonal Number
- no
- Hexagonal Number
- no
- Lucas Number
- no
- Tetrahedral Number
- no
- Pell Number
- no
- Tribonacci Number
- no
- Pronic Number
- no
Recreational
- Happy Number
- no
- Harshad Number
- yes
- Narcissistic Number
- no
- Collatz Steps
- 45
- Smith Number
- no
- Vampire Number
- no
Primality
- Prime
- no
- Composite Number
- yes
- Semiprime
- no
- Squarefree Number
- no
- Prime Power
- no
- Prime Factorization
- no
- Twin Prime
- no
- Mersenne Prime
- no
- Sophie Germain Prime
- no
- Safe Prime
- no
- Powerful Number
- no
- Achilles Number
- no
- Perfect Power
- no
- Smooth Number
- no
- Carmichael Number
- no
Classification
- Even
- yes
- Odd
- no
Appears in sequences
- Coefficients of Jacobi cusp form of index 1 and weight 12.at n=17A003785
- Weighted count of partitions with distinct parts.at n=36A005895
- a(n) = (n+1)*(n^2+n+2)/2; g.f.: (1 + 2*x^2) / (1 - x)^4.at n=29A006000
- Aliquot sequence starting at 1074.at n=6A014364
- a(n) = number of (s(0), s(1), ..., s(n)) such that every s(i) is an integer, s(0) = 0, |s(i) - s(i-1)| = 1 for i = 1,2; |s(i) - s(i-1)| <= 1 for i >= 3, s(n) = 4. Also a(n) = T(n,n-4), where T is the array defined in A024996.at n=8A026071
- Triangle: a(n,m) = number of permutations of (1,2,...,n) with one or more fixed points in the m first positions.at n=30A061018
- Numbers k such that sigma(k)+1 is a square and sets a new record for such squares.at n=33A063729
- First differences of A069474, successive differences of (n+1)^6-n^6.at n=4A069475
- a(n) = 9*n^3 - 18*n^2 + 10*n.at n=12A086605
- a(n) = (3+n)*(2 + 33*n + n^2)/6.at n=33A101860
- a(n) = n*(8*n+7).at n=40A139278
- Maximal length of rook tour on an n X n+2 board.at n=25A152133
- Triangle t(n,k) read by rows: fibonomial ratios c(n)/(c(k)*c(n-k)) where c are partial products of a generalized Fibonacci sequence with multiplier m=3.at n=25A172339
- Triangle t(n,k) read by rows: fibonomial ratios c(n)/(c(k)*c(n-k)) where c are partial products of a generalized Fibonacci sequence with multiplier m=3.at n=23A172339
- Second beta integer combination triangle of a Narayana type: a=3:f(n, a) = a*f(n - 1, a) + f(n - 2, a);c(n,a)=If[n == 0, 1, Product[f(i, a), {i, 1, n}]];w(n,m,q)=c(n - 1, q)*c(n, q)/(c(m - 1, q)*c(n - m, q)*c(m - 1, q)*c(n - m + 1, q)*f(m, q)).at n=16A172378
- Second beta integer combination triangle of a Narayana type: a=3:f(n, a) = a*f(n - 1, a) + f(n - 2, a);c(n,a)=If[n == 0, 1, Product[f(i, a), {i, 1, n}]];w(n,m,q)=c(n - 1, q)*c(n, q)/(c(m - 1, q)*c(n - m, q)*c(m - 1, q)*c(n - m + 1, q)*f(m, q)).at n=19A172378
- a(n) = 2^n*C(n-1) - A186997(n-1), where C(n) are the Catalan numbers (A000108).at n=6A192479
- Number of nX1 0..3 arrays with values 0..3 introduced in row major order, the number of instances of each value within one of each other, and every element equal to zero or one horizontal or vertical neighbors.at n=10A199350
- Triangle read by rows: T(n,k) (1 <= k <= n) = number of irreducible coverings by edges of the complete bipartite graph K_{n,k}.at n=19A210654
- Smallest number k such that prime(n) divides the n-th divisor of k.at n=27A226101